For closed \(A\subset \mathbb {R}^n\) , the inner \(\alpha \) -Riesz equilibrium measure \(\gamma _A\)  can alternatively be characterized as the only measure in \(\mathcal {E}^+_A\)  satisfying (). But if \(A\)  is not closed, \(\gamma _A\)  may not be concentrated on the set \(A\)  itself, but on \(\overline{A}\) , the closure of \(A\)  in \(\mathbb {R}^n\) ; and moreover, there is in general no \(\nu \in \mathcal {E}^+_A\)  having the property \(\kappa _\alpha \nu =1\)  n.e. on \(A\) . Regarding the latter, see [1]} (Theorem 1.1(e) and footnote 3).
